Myanmar's opposition party, led by Nobel laureate Aung San Suu Kyi, has secured a historic majority in the country's parliament, the country's election commission confirmed Friday.

The tally from Sunday's vote was still being counted and final results were not expected for several days, but the commission said that Suu Kyi's National League for Democracy (NLD) party had passed the required threshold of 329 seats for a majority in the 664-member, two-house Parliament. A party with a combined parliamentary majority is able to select the next president, who can then name a Cabinet and form a new government.

The NLD has officially won 238 seats in the lower house -- which means it now will have the power to pass bills -- and 110 in the upper house, for a total of 348.

In comparison, the ruling pro-military Union Solidarity and Development Party (USDP) has won 40 seats, according to the latest results Friday afternoon.

The results mean that Myanmar is likely to soon have its first government in decades that isn't under the military's sway. But while an NLD majority assures it of being able to elect the president, Suu Kyi remains barred from the office by a constitutional provision inserted by the military before it transferred power to Thein Sein's quasi-civilian government in 2011.

Suu Kyi has declared, however, that she will become the country's de facto leader, acting "above the president" if her party forms the next government, and that the new president will be a figurehead.

While the army has not conceded defeat for the USDP, it has acknowledged the massive success of Suu Kyi's National League for Democracy in Sunday's election, and pledged it will respect the final results.

Suu Kyi's party said it received a message Wednesday from Information Minister Ye Htut on behalf of President Thein Sein congratulating it for leading the race for parliamentary seats.

Ye Htut said the government will pursue a peaceful transfer of power "in accordance with the legislated timeline." He was not immediately available for comment.

The message helps ease lingering concerns that the military might deny the NLD power, as it did after the party won a landslide election victory in 1990.

President Barack Obama congratulated Suu Kyi for her party's success in the elections.

In a phone call, Obama commended Suu Kyi for "her tireless efforts and sacrifice over so many years" to promote a peaceful, democratic Myanmar, the White House said.

Obama also called Thein Sein to congratulate the country on its success in conducting the elections and stressed the importance of respecting the outcome, it said.

Ben Rhodes, Obama's deputy national security adviser, told reporters Thursday that Suu Kyi "is in a very strong position as the leader of the NLD to be a leading voice about the future direction of the country." He said it would be up to Myanmar's new parliament and leaders to decide about constitutional reform.

Myanmar's military, which took power in a 1962 coup and brutally suppressed several pro-democracy uprisings during its rule, gave way to Thein Sein's nominally civilian elected government in 2011 — with strings attached.

It installed retired senior officers in the ruling party to fill Cabinet posts and gave itself key powers in the constitution, including control of several powerful ministries and a quarter of the seats in both houses of Parliament. In a state of emergency, a special military-led body can even assume state powers. Another provision bars Suu Kyi from the presidency because her sons hold foreign citizenship.

While Myanmar's people voted overwhelmingly Sunday to remove the military-backed ruling party from power, it's clear that the army's involvement in politics won't end, and the NLD will need to convince it to cooperate.

The Associated Press contributed to this report.